Modular Arithmetic with Nodal Lines: Drumhead Surface States in ZrSiTe

We study the electronic structure of the nodal line semimetal ZrSiTe both experimentally and theoretically. We find two different surface states in ZrSiTe—topological drumhead surface states and trivial floating band surface states, which can be easily distinguished in ARPES experiments. Using the spectra of Wilson loops, we show that a nontrivial Berry phase that exists in a confined region within the Brillouin zone gives rise to the topological drumhead-type surface states. The Z_{2} structure of the Berry phase induces a Z_{2} “modular arithmetic” of the surface states, allowing surface states derived from different nodal lines to hybridize and gap out, which can be probed by a set of Wilson loops. Our findings are confirmed by ab initio calculations and angle-resolved photoemission experiments, which are in excellent agreement with each other and the topological analysis. This work is the first complete characterization of topological surface states in the family of square-net-based nodal line semimetals, and thus it fundamentally increases the understanding of the topological nature of this growing class of topological semimetals